Author ORCID Identifier
Bachelor of Arts
Elizabeth L. Wilmer
Spectral graph theory, Eigenvalues, Interlacing inequalities
Motivated by an effort to simplify the Watts-Strogatz model for small-world networks, we generalize a theorem concerning interlacing inequalities for the eigenvalues of the normalized Laplacians of two graphs differing by a single edge. Our generalization allows weighted edges and certain instances of self loops. These inequalities were first proved by Chen et. al in  but our argument generalizes the simplified argument given by Li in .
Pieper, Hannah E., "Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities" (2018). Honors Papers. 171.